Expression of type ExprTuple ¶

from the theory of proveit.physics.quantum.QPE ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import ExprRange, ExprTuple, Variable, VertExprArray, e, l
from proveit.logic import Union
from proveit.numbers import Abs, Add, Exp, Interval, ModAbs, Sum, greater, one, two
from proveit.physics.quantum import NumKet, Z, ket_plus
from proveit.physics.quantum.QPE import ModAdd, QPE, _U, _b_floor, _ket_u, _neg_domain, _pos_domain, _rel_indexed_alpha, _s, _s_wire, _t, _two_pow_t
from proveit.physics.quantum.circuits import Gate, Input, Measure, MultiQubitElem, Output, Qcircuit
from proveit.statistics import ProbOfAll

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr2 = [l]
sub_expr3 = Add(_t, one)
sub_expr4 = Add(_t, _s)
sub_expr5 = Interval(sub_expr3, sub_expr4)
sub_expr6 = MultiQubitElem(element = Gate(operation = QPE(_U, _t), part = sub_expr1), targets = Interval(one, sub_expr4))
sub_expr7 = Qcircuit(vert_expr_array = VertExprArray([ExprRange(sub_expr1, Input(state = ket_plus), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Input(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)], [ExprRange(sub_expr1, sub_expr6, one, _t), ExprRange(sub_expr1, sub_expr6, sub_expr3, sub_expr4)], [ExprRange(sub_expr1, Measure(basis = Z), one, _t), _s_wire], [ExprRange(sub_expr1, MultiQubitElem(element = Output(state = NumKet(ModAdd(_b_floor, l), _t), part = sub_expr1), targets = Interval(one, _t)), one, _t), ExprRange(sub_expr1, MultiQubitElem(element = Output(state = _ket_u, part = sub_expr1), targets = sub_expr5), one, _s)]))
expr = ExprTuple(ProbOfAll(instance_param_or_params = sub_expr2, instance_element = sub_expr7, domain = Union(_neg_domain, _pos_domain), condition = greater(ModAbs(l, _two_pow_t), e)), Add(Sum(index_or_indices = sub_expr2, summand = Exp(Abs(_rel_indexed_alpha), two), domain = _neg_domain), ProbOfAll(instance_param_or_params = sub_expr2, instance_element = sub_expr7, domain = _pos_domain)))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\textrm{Prob}_{l \in \{-2^{t - 1} + 1~\ldotp \ldotp~-\left(e + 1\right)\} \cup \{e + 1~\ldotp \ldotp~2^{t - 1}\}~|~\left|l\right|_{\textup{mod}\thinspace 2^{t}} > e}~\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right), \left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \left|\alpha_{b_{\textit{f}} \oplus l}\right|^{2}\right) + \left[\textrm{Prob}_{l \in \{e + 1~\ldotp \ldotp~2^{t - 1}\}}~\left(\begin{array}{c} \Qcircuit@C=1em @R=.7em{
\qin{\lvert + \rangle} & \multigate{4}{\textrm{QPE}\left(U, t\right)} & \meter & \multiqout{3}{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} & \ghost{\textrm{QPE}\left(U, t\right)} & \measure{\begin{array}{c}:\\ \left(t - 3\right) \times \\:\end{array}} \qw & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert + \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & \meter & \ghostqout{\lvert b_{\textit{f}} \oplus l \rangle_{t}} \\
\qin{\lvert u \rangle} & \ghost{\textrm{QPE}\left(U, t\right)} & { /^{s} } \qw & \qout{\lvert u \rangle}
} \end{array}\right)\right]\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

	core type	sub-expressions
0	ExprTuple	1, 2
1	Operation	operator: 11 operand: 5
2	Operation	operator: 144 operands: 4
3	ExprTuple	5
4	ExprTuple	6, 7
5	Lambda	parameter: 147 body: 8
6	Operation	operator: 9 operand: 14
7	Operation	operator: 11 operand: 15
8	Conditional	value: 25 condition: 13
9	Literal
10	ExprTuple	14
11	Literal
12	ExprTuple	15
13	Operation	operator: 16 operands: 17
14	Lambda	parameter: 147 body: 18
15	Lambda	parameter: 147 body: 20
16	Literal
17	ExprTuple	21, 22
18	Conditional	value: 23 condition: 24
19	ExprTuple	147
20	Conditional	value: 25 condition: 26
21	Operation	operator: 34 operands: 27
22	Operation	operator: 28 operands: 29
23	Operation	operator: 135 operands: 30
24	Operation	operator: 34 operands: 31
25	Operation	operator: 32 operands: 33
26	Operation	operator: 34 operands: 35
27	ExprTuple	147, 36
28	Literal
29	ExprTuple	128, 37
30	ExprTuple	38, 140
31	ExprTuple	147, 57
32	Literal
33	ExprTuple	39, 40, 41, 42
34	Literal
35	ExprTuple	147, 58
36	Operation	operator: 43 operands: 44
37	Operation	operator: 45 operands: 46
38	Operation	operator: 47 operand: 60
39	ExprTuple	49, 50
40	ExprTuple	51, 52
41	ExprTuple	53, 54
42	ExprTuple	55, 56
43	Literal
44	ExprTuple	57, 58
45	Literal
46	ExprTuple	147, 59
47	Literal
48	ExprTuple	60
49	ExprRange	lambda_map: 61 start_index: 152 end_index: 148
50	ExprRange	lambda_map: 62 start_index: 152 end_index: 139
51	ExprRange	lambda_map: 63 start_index: 152 end_index: 148
52	ExprRange	lambda_map: 63 start_index: 125 end_index: 126
53	ExprRange	lambda_map: 64 start_index: 152 end_index: 148
54	ExprRange	lambda_map: 65 start_index: 152 end_index: 139
55	ExprRange	lambda_map: 66 start_index: 152 end_index: 148
56	ExprRange	lambda_map: 67 start_index: 152 end_index: 139
57	Operation	operator: 116 operands: 68
58	Operation	operator: 116 operands: 69
59	Operation	operator: 135 operands: 70
60	Operation	operator: 71 operand: 138
61	Lambda	parameter: 124 body: 73
62	Lambda	parameter: 124 body: 74
63	Lambda	parameter: 124 body: 75
64	Lambda	parameter: 124 body: 76
65	Lambda	parameter: 124 body: 77
66	Lambda	parameter: 124 body: 78
67	Lambda	parameter: 124 body: 80
68	ExprTuple	81, 82
69	ExprTuple	105, 127
70	ExprTuple	140, 148
71	Literal
72	ExprTuple	138
73	Operation	operator: 108 operands: 83
74	Operation	operator: 90 operands: 84
75	Operation	operator: 90 operands: 85
76	Operation	operator: 86 operands: 87
77	Operation	operator: 109 operands: 88
78	Operation	operator: 90 operands: 89
79	ExprTuple	124
80	Operation	operator: 90 operands: 91
81	Operation	operator: 144 operands: 92
82	Operation	operator: 150 operand: 105
83	NamedExprs	state: 94
84	NamedExprs	element: 95 targets: 103
85	NamedExprs	element: 96 targets: 97
86	Literal
87	NamedExprs	basis: 98
88	NamedExprs	operation: 99
89	NamedExprs	element: 100 targets: 101
90	Literal
91	NamedExprs	element: 102 targets: 103
92	ExprTuple	104, 152
93	ExprTuple	105
94	Operation	operator: 106 operand: 120
95	Operation	operator: 108 operands: 115
96	Operation	operator: 109 operands: 110
97	Operation	operator: 116 operands: 111
98	Literal
99	Literal
100	Operation	operator: 114 operands: 112
101	Operation	operator: 116 operands: 113
102	Operation	operator: 114 operands: 115
103	Operation	operator: 116 operands: 117
104	Operation	operator: 150 operand: 127
105	Operation	operator: 144 operands: 119
106	Literal
107	ExprTuple	120
108	Literal
109	Literal
110	NamedExprs	operation: 121 part: 124
111	ExprTuple	152, 126
112	NamedExprs	state: 122 part: 124
113	ExprTuple	152, 148
114	Literal
115	NamedExprs	state: 123 part: 124
116	Literal
117	ExprTuple	125, 126
118	ExprTuple	127
119	ExprTuple	128, 152
120	Literal
121	Operation	operator: 129 operands: 130
122	Operation	operator: 131 operands: 132
123	Literal
124	Variable
125	Operation	operator: 144 operands: 133
126	Operation	operator: 144 operands: 134
127	Operation	operator: 135 operands: 136
128	Variable
129	Literal
130	ExprTuple	137, 148
131	Literal
132	ExprTuple	138, 148
133	ExprTuple	148, 152
134	ExprTuple	148, 139
135	Literal
136	ExprTuple	140, 141
137	Literal
138	Operation	operator: 142 operands: 143
139	Literal
140	Literal
141	Operation	operator: 144 operands: 145
142	Literal
143	ExprTuple	146, 147
144	Literal
145	ExprTuple	148, 149
146	Literal
147	Variable
148	Literal
149	Operation	operator: 150 operand: 152
150	Literal
151	ExprTuple	152
152	Literal

Expression of type ExprTuple¶

from the theory of proveit.physics.quantum.QPE¶

Expression of type ExprTuple ¶

from the theory of proveit.physics.quantum.QPE ¶